Question

Given: ΔABC is a right triangle.
Prove: a2 + b2 = c2

Answer 1

The two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles:


Statement Justification
Draw an altitude from point C to Line segment AB
Let segment BC = a
segment CA = b
segment AB = c
segment CD = h
segment DB = x
segment AD = y
y + x = c
c over a equals a over y and c over b equals b over x
a2 = cy; b2 = cx
a2 + b2 = cy + b2
a2 + b2 = cy + cx
a2 + b2 = c(y + x)
a2 + b2 = c(c)
a2 + b2 = c2


Which is not a justification for the proof?
Addition Property of Equality
Pythagorean Theorem
Pieces of Right Triangles Similarity Theorem
Cross Product Property